Run for Cover: Dominating Set via Mobile Agents

Document Type

Conference Article

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Abstract

Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network problems using mobile agents. In this paper, we study one such problem– finding small dominating sets of a graph G using mobile agents. Dominating set is interesting in the field of mobile agents as it opens up a way for solving various robotic problems, e.g., guarding, covering, facility location, transport routing, etc. In this paper, we first present two algorithms for computing a minimal dominating set: (i) an O(m) time algorithm if the robots start from a single node (i.e., gathered initially), (ii) an O(ℓΔlog (λ) + nℓ+ m) time algorithm, if the robots start from multiple nodes (i.e., positioned arbitrarily), where m is the number of edges and Δ is the maximum degree of G, ℓ is the number of clusters of the robots initially and λ is the maximum ID-length of the robots. Then we present a ln (Δ) approximation algorithm for the minimum dominating set which takes O(nΔlog (λ) ) rounds.

First Page

133

Last Page

150

DOI

10.1007/978-3-031-48882-5_10

Publication Date

1-1-2023

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